Rectangle interface

data Rectangle = Rect Int Int Int Int

 {- The empty rectangle -}
emptyRect :: Rectangle

 {- Create a rectangle given lower lefthand corner and size -}
rect      :: Coord -> Size  -> Rectangle
 {- Create rectangle using extremes as boundary points -}
absRect   :: Coord -> Coord -> Rectangle

 {- Return the smallest rectangle that encompasses both rects -}
unionRects      :: Rectangle -> Rectangle   -> Rectangle

 {- Move the rectangle along -}
translateRect   :: Translation -> Rectangle -> Rectangle

 {- Apply transform to rectangle -}
transformRect   :: Transform -> Rectangle   -> Rectangle

 {- a weaker form of transexampleion -}
scaleRotateRect :: Transform -> Rectangle   -> Rectangle

 {- do the two rects intersect? -}
intersectRects  :: Rectangle -> Rectangle   -> Maybe Rectangle

 {- point on the inside? -}
pointInRect     :: Coord -> Rectangle -> Bool

 {- augment rectangle so that it also includes point -}
addRectCoord    :: Coord -> Rectangle -> Rectangle
  {-
    resizes the rectangle, using the direction value
    to indicate the origin for the scaling operation.
  -}
resizeRect :: CompassDirection -> Size -> Rectangle -> Rectangle

 {- return 'da size -}
rectSize :: Rectangle -> Size
 {- Lower left and upper right hand corners -}
rectLL   :: Rectangle -> Coord
rectUR   :: Rectangle -> Coord

 {- return the coord that is spot in the middle -}
middlePoint :: Rectangle -> Coord

 {- return the point that corres. to one of the directions
    (modulo rounding errors, o.c.) -}
dirCoord    :: CompassDirection -> Rectangle -> Coord

 {- convert coordinate from the rectangles c. system to global -}
localToGlobal :: Rectangle  -> Coord -> Coord
 {- other way around -}
globalToLocal :: Rectangle  -> Coord -> Coord